1. ELECTRIC CIRCUITS EIGHTH EDITION
JAMES W. NILSSON
&
SUSAN A. RIEDEL
ELECTRIC CIRCUITS EIGHTH EDITION

2. CHAPTER 18
TWO-PORT CIRCUITS
© 2008 Pearson Education

3. CONTENTS 18.1 The Terminal Equations 18.2 The Two-Port Parameters
18.3 Analysis of the Terminated Two-Port Circuit
18.4 Interconnected Two-Port Circuits
© 2008 Pearson Education

4. 18.1 The Terminal Equations
Two-Port Model
The two-port model is used to describe the performance of a circuit in terms of the voltage and current at its input and output ports.
© 2008 Pearson Education

5. 18.1 The Terminal Equations
The two-port building block
© 2008 Pearson Education

6. 18.1 The Terminal Equations
The s-domain two-port basic building block
© 2008 Pearson Education

7. 18.1 The Terminal Equations
The model is limited to circuits in which:
No independent sources are inside the circuit between the ports.
No energy is stored inside the circuit between the ports.
© 2008 Pearson Education

8. 18.1 The Terminal Equations
The current into the port is equal to the current out of the port.
No external connections exist between the input and output ports.
© 2008 Pearson Education

9. 18.1 The Terminal Equations
Two of the four terminal variables (V1, I1, V2, I2) are independent; therefore, only two simultaneous equations involving the four variables are needed to describe the circuit.
© 2008 Pearson Education

10. 18.1 The Terminal Equations
The six possible sets of simultaneous equations involving the four terminal variables are called the z-, y-, a-, b-, h-, and g-parameter equations.
© 2008 Pearson Education

11. 18.1 The Terminal Equations
© 2008 Pearson Education

12. 18.1 The Terminal Equations
© 2008 Pearson Education

13. 18.1 The Terminal Equations
© 2008 Pearson Education

14. 18.1 The Terminal Equations
The parameter equations are written in the s domain.
The dc values of the parameters are obtained by setting s = 0, and the sinusoidal steady-state values are obtained by setting s = j.
© 2008 Pearson Education

15. 18.2 The Two-Port Parameters
Any set of parameters may be calculated or measured by invoking appropriate short-circuit and open-circuit conditions at the input and output ports.
© 2008 Pearson Education

16. 18.2 The Two-Port Parameters
© 2008 Pearson Education

17. 18.2 The Two-Port Parameters
Example: Finding the z Parameters of a Two-Port Circuit.
Find the z parameters for the circuit shown in below.
© 2008 Pearson Education

18. 18.2 The Two-Port Parameters
The relationships among the six sets of parameters are given in this table:
Parameter conversion table
© 2008 Pearson Education

19. 18.2 The Two-Port Parameters
A two-port circuit is reciprocal if the interchange of an ideal voltage source at one port with an ideal ammeter at the other port produces the same ammeter reading.
© 2008 Pearson Education

20. 18.2 The Two-Port Parameters
The effect of reciprocity on the two-port parameters is given by:
© 2008 Pearson Education

21. 18.2 The Two-Port Parameters
A reciprocal two-port circuit
© 2008 Pearson Education

22. 18.2 The Two-Port Parameters
A reciprocal two-port circuit is symmetric if its ports can be interchanged without disturbing the values of the terminal currents and voltages.
A circuit with the voltage source and ammeter interchanged
© 2008 Pearson Education

23. 18.2 The Two-Port Parameters
Four examples of symmetric two-port circuits.
A symmetric tee
A symmetric pi
© 2008 Pearson Education

24. 18.2 The Two-Port Parameters
A symmetric bridged tee
A symmetric lattice
© 2008 Pearson Education

25. 18.3 Analysis of the Terminated Two-Port Circuit
To illustrate how the six characteristics are derived, we develop the expressions using the z parameters to model the two-port portion of the circuit.
The next tables summarize the expressions involving the y, a, b, h, and g parameters.
© 2008 Pearson Education

26. 18.3 Analysis of the Terminated Two-Port Circuit
Terminated two-port equations
© 2008 Pearson Education

27. 18.3 Analysis of the Terminated Two-Port Circuit
Terminated two-port equations
© 2008 Pearson Education

28. 18.3 Analysis of the Terminated Two-Port Circuit
Terminated two-port equations
© 2008 Pearson Education

29. 18.3 Analysis of the Terminated Two-Port Circuit
Example: Analyzing a Terminated Two-Port Circuit.
The two-port circuit shown below is described in terms of its b parameters, the values of which are
b11 = -20, b12 = -3000Ω,
b21 = -2mS, b22 = -0.2
Find the phasor voltage V2.
Find the average power delivered to the 5kΩ load.
Find the average power delivered to the input port.
Find the load impedance for maximum average power transfer.
Find the maximum average power delivered to the load in (d).
© 2008 Pearson Education

30. 18.4 Interconnected Two-Port Circuits
Large networks can be divided into subnetworks by means of interconnected two-port models.
© 2008 Pearson Education

31. 18.4 Interconnected Two-Port Circuits
(a) Cascade
(b) Series
(c) Parallel
© 2008 Pearson Education

32. 18.4 Interconnected Two-Port Circuits
(d) Series-parallel
(e) Parallel-series
© 2008 Pearson Education

33. 18.4 Interconnected Two-Port Circuits
A cascade connection
© 2008 Pearson Education

34. THE END
© 2008 Pearson Education